To show that a proposition is a false proposition, we can usually give an example to make it have the conditions of the proposition, not the conclusion of the proposition. This example is called counterexample.

In mathematics, counterexamples are often used to prove. There are many mathematical conjectures or propositions that are full-name propositions, claiming that all things have certain properties, or that certain results will be obtained as long as certain conditions are met. When it is difficult to prove such a mathematical conjecture, mathematicians tend to find a counterexample to show that this conjecture is wrong.

In addition, some counterexamples can help people better understand the essence of some mathematical concepts. This is because the existence of counterexamples shows that some things A satisfy the condition P, but have no property Q, which can avoid the wrong results caused by using full name reasoning.

Extended data

The application of counterexample in philosophy;

In philosophy, most conclusions and inferences are extensive and cannot be strictly proved as in mathematics. Therefore, the construction of counterexamples is mainly to show that a certain philosophical theory or assertion cannot be applied to a special situation. A famous example is the Gettier problem.

For a long time, the concept of knowledge in western philosophy can be summarized as the so-called JTB theory, that is, the proven true belief. In the1960s, Gettier published a paper, which questioned this definition and gave counterexamples, which made the definition of knowledge become a topic of philosophical discussion again.

Baidu Encyclopedia-Counterexample